Thomas Rode Andersen has looked to the Palaeolithic period for his new fast-food reataurant, Pæleo, soon to open in Copenhagen.

There will be hot dogs and pizzas, but no buns or dough; meat, fish, berries and vegetables, but no starch, refined sugars or dairy products. This is fast food that's fit for a caveman.

While modern Nordic cuisine has catapulted the Danish capital to the top of the culinary world, the chef behind takeaway restaurant Palæo looked for inspiration from the stone age – or palaeolithic period – to create "primal gastronomy".

"Bread is the devil," says Thomas Rode Andersen, 43, who has created the menu for Palæo and is head chef at the Michelin-starred Kong Hans in Copenhagen. After divorcing in 2005 he started dating a younger woman and swapped late-night beers and snacks for "paleo" food and exercise.

In the last couple of years he has become something of a poster boy for the paleo movement in Denmark, but he still allows himself the odd break from the diet.

"There is room for a glass of red wine once in a while. If I want to smoke a cigarette I will do that but there might be two months in between," says Andersen.

"For me it now becomes a rich sensory experience to sit down on a Sunday and eat a piece of rye bread with pickled herring and have a glass of schnapps."

Andersen hopes his takeaway, which opens in Copenhagen within weeks, will inspire people to try a healthy alternative to standard fast food.

The menu includes "meatza", essentially a meat pizza turned upside down with a base of organic ground beef topped with baked tomatoes, pickled mushrooms and parsley pesto. For the hot dog, the sausage with wild leeks comes in an egg-based wrapper, while the risotto is made of small kernels of celeriac shaped to look like long-grain rice.

Andersen cherishes the challenge of cooking modern food under paleo rules. "Making Tournedos Rossini is dead easy. You just buy some foie gras, some truffles and fry some bread and beef fillet. That's not hard. It's harder to create two desserts without sugar."

For the menu at Palæo he uses ripe pears to sweeten the puddings.Berlin lays claim to having Europe's first paleo restaurant, which opened last year, and the diet has had a large following in the US and among practitioners of the CrossFit training programme.

Some critics say the original caveman diet was more varied than suggested, pointing to archaeological studies that show traces of grains found on grinding stones dating back 30,000 years.

Cornell McClellan, who is the personal fitness trainer for Barack Obama, also questions whether it is possible to mimic a prehistoric diet. In an article for the Chicago Sun Times, McClellan wrote: "Our stone age ancestors were not eating factory farmed meat, which is full of chemicals and hormones. Unless you have a spear handy and access to unlimited buffalo, you are going to have a hard time truly eating like a caveman."

Andersen says he is fed up with being known as the "stone-age chef", but believes he has a duty to champion the diet because too many people walk around "feeling like hell".

"It's all about going back to something original, going back to what we are designed to eat and the way our bodies are designed to work, and nothing to do with what we have come up with in the interim 10,000-12,000 years."